College Algebra MATH 107
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MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #112 are Multiple Choice.
Problems #1321 are Short Answer. (Work not required to be shown)
Problems #2230 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function
2. Solve: 11+ 2x = x 2
3. Determine the interval(s) on which the function is increasing.
4. Determine whether the graph of y = 9+ x is symmetric with respect to the origin,
the x-axis, or the y-axis.
5. Solve, and express the answer in interval notation: | 5 6x | £ 13.
6. Which of the following represents the graph of 2x 7y = 14 ?
7. Write a slope-intercept equation for a line parallel to the line x 4y = 6 which passes through
the point (8, 3).
8. Which of the following best describes the graph?
9. Express as an equivalent expression: 3 log y + log 1 log (x + 2)
10. Which of the functions corresponds to the graph?
11. Suppose that a function f has no x-intercepts. Which of the following statements MUST be true?
12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No
formulas are given.) What is the relationship between g(x) and f (x)?
13. Multiply and simplify: (8 + 3i)(2 + 5i). Write the answer in the form a + bi, where a and b are real numbers
14. Solve, and write the answer in interval notation:
15. A can of soda at 82° F. is placed in a refrigerator that maintains a constant temperature of 35°
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 35 + 47 e 0.058 t Find the temperature of the soda 10 minutes after it is placed in the refrigerator. (Round to the
nearest tenth of a degree.)
16. Find the value of the logarithm
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x + 3 and g (x) = x 5.
(a) Find ) . Show work.
(b) Find the domain of the quotient function
g
f
. Explain.
24. Find the equation for a line which passes through the points (5, 2) and (8, 7). Write the
equation in slope-intercept form. Show work.
25. A salesperson earns a base salary of $1,475 per month and a commission of 8.4% on the
amount of sales. If the salesperson has a paycheck of $4,637.60 for one month, what was the
amount of sales for the month? Show work.
26. Let f (x) = 5×2 4 and g(x) = x 2.
(a) Find the composite function ( f o g)(x) and simplify. Show work.
(b) Find ( f o g ) (2) . Show work.
27. Find the exact solutions and simplify as much as possible: 8×2 = 6x + 1. Show work.
28. Given the function
1
( ) 4
7
f x = x , find a formula for the inverse function. Show work.
Summer, 2020
23. Points (2, 1) and (6, 5) are endpoints of a line segment.
(a) What is the length of the line segment? Give the exact answer, no decimals, simplified as
much as possible. Show work.
(b) What is the midpoint M of the line segment?
Both parts of this problem are asking for composition
or evaluation of functions, not multiplication.
(c) Given the point M you found in part (b), state the point symmetric to M about the y-axis.
Do not multiply here. Evaluate the quotient function.
College Algebra MATH 107
